Question: Simplify the following expression: $\dfrac{14x^4}{6x^3}$ You can assume $x \neq 0$.
Answer: $ \dfrac{14x^4}{6x^3} = \dfrac{14}{6} \cdot \dfrac{x^4}{x^3} $ To simplify $\frac{14}{6}$ , find the greatest common factor (GCD) of $14$ and $6$ $14 = 2 \cdot 7$ $6 = 2 \cdot 3$ $ \mbox{GCD}(14, 6) = 2 $ $ \dfrac{14}{6} \cdot \dfrac{x^4}{x^3} = \dfrac{2 \cdot 7}{2 \cdot 3} \cdot \dfrac{x^4}{x^3} $ $\phantom{ \dfrac{14}{6} \cdot \dfrac{4}{3}} = \dfrac{7}{3} \cdot \dfrac{x^4}{x^3} $ $ \dfrac{x^4}{x^3} = \dfrac{x \cdot x \cdot x \cdot x}{x \cdot x \cdot x} = x $ $ \dfrac{7}{3} \cdot x = \dfrac{7x}{3} $